One guys says: "It's not part of our culture to think about the past, we think about the future"
then another guy (telling someone about the first guy) says: "I thought grace was a Judaeo - Christian idea, but he really did mean it"

--- I understand that the second guy says that he knows that being a Judaeo Christian is important and it is a kind of grace, but that guy really lived according to the rules of Judaeo - Christian ideas.

It's hard for me to give you a good explanation without more context - is the first guy saying that he looks toward the future as an explanation of why he is able to forgive someone, perhaps? Anyway, "grace" is a concept that has occupied great theologians and entire volumes. Grace is a gift, given freely by God. Martin Luther claimed that our salvation comes directly through God's grace and does not depend on anything that a priest does at church (see Reformation, Protestan). A more modern take on grace is the ubiquitous bumper sticker "Grace Happens," a playful spin on the popular saying, "Sh*t Happens."
All this to say that the second guy is not saying that being a faithful believer in the Judaeo-Christian deity is important, but more likely either a) the first guy shows that receiving God's grace has transformed his life, or b) that the first guy, like God, is bestowing the gift of grace on others.
Hope this has been helpful---
Site Hint: Check out our list of pronunciation videos.

I'll give you a bit more context Emotion: smile

The Japanese guy says that after fire bombing of Tokyo (in which almost his whole family died) he went on to work as an interpreter at an American base.
The guy who is listening to him is very surprised and says that Americans killed your whole family and you went to work for them. Then the Japanese guy says that in their culture they think about the future not about the past. And then the guy who was listening to him says (telling this story to someone else): "I thought grace........."

Is it clearer now Emotion: smile So, what exactly he meant by saying this: "I thought grace...."
The Japanese man, by not only forgiving the country who killed his family but by going on to help Americans with their work, has demonstrated the quality of grace. The speaker had thought that the ability to forgive such a grave injury, and to forgive it completely, could only result from believing in the power of the Western God's grace (or at least with a cultural familiarity with the concept). However, a Japanese man, who presumably is not a Christian and does not live in a Judaeo-Christian influenced culture, is behaving in a way that most American Christians would find hard to emulate, however much lip service they might pay to the doctrine of "...and forgive us our trespasses, as we forgive those who trespass against us."
Peace to you, Newguest Emotion: smile
Thank you for your clarifications Delmobile
Students: We have free audio pronunciation exercises.